Factoring higher-degree polynomials Video transcript Plot the real zeroes of the given polynomial on the graph below. And they give us p of x is equal to 2 x to the 5th plus x to the 4th minus 2x minus 1.
Dividing polynomials with remainders Video transcript Simplify the expression 18x to the fourth minus 3x squared plus 6x minus 4, all of that over 6x. So there's a couple ways to think about them. They're all really equivalent.
You can really just view this up here as being the exact same thing as 18x to the fourth over 6x plus negative 3x squared over 6x, or you could say minus 3x squared over 6x, plus 6x over 6x, minus 4 over 6x.
Now, there's a couple of ways to think about it. One is I just kind of decomposed this numerator up here. Or maybe not so clearly, but hopefully that helps clarify it. Another way to think about it is kind of like you're distributing the division.
If I divide a whole expression by something, that's equivalent to dividing each of the terms by that something. The other way to think about it is that we're multiplying this entire expression.
So this is the same thing as 1 over 6x times this entire thing, times 18x to the fourth minus 3x squared plus 6x minus 4.
And so here, this would just be the straight distributive property to get to this. Whatever seems to make sense for you-- they're are all equivalent.
They're all logical, good things to do to simplify this thing. Now, once you have it here, now we just have a bunch of monomials that we're just dividing by 6x.
And here, we could just use exponent properties. This first one over here, we can take the coefficients and divide them. And then you have x to the fourth divided by x to the-- well, they don't tell us. But if it's just an x, that's the same thing as x to the first power.
So it's x to the fourth divided by x to the first. That's going to be x to the 4 minus 1 power, or x to the third power. Then we have this coefficient over here, or these coefficients.
We have negative 3 divided by 6. So I'm going to do this part next. And then you have x squared divided by x. We already know that x is the same thing as x to the first. So that's going to be x to the 2 minus 1 power, which is just 1. Or I could just leave it as an x right there.
Then we have these coefficients, 6 divided by 6. Well, that's just 1. So I could just-- well, I'll write it. I could write a 1 here. And let me just write the 1 here, because we said 2 minus 1 is 1.
And then x divided by x is x to the first over x to the first. You could view it two ways-- anything divided by anything is just 1. Or you could view it as x to the 1 divided by x to the 1 is going to be x to the 1 minus 1, which is x to the 0, which is also equal to 1.
Either way, you knew how to do this before you even learned that exponent property. Because x divided by x is 1, and then assuming x does not equal to 0. And we kind of have to assume x doesn't equal 0 in this whole thing. Otherwise, we would be dividing by 0.
And then finally, we have 4 over 6x. And there's a couple of ways to think about it. Just simplified that fraction. Another way to think about it is you could have viewed this 4 as being multiplied by x to the 0 power, and this being x to the first power.Jan 13, · Best Answer: "Third degree" means the highest exponential power is 3, and "monomial" means only one term.
So 5x^3 is an example of a third-degree monomial. Binomials have two terms ("bi" means 2). So a fourth degree binomial could be x^4 - 7 I'm Status: Resolved.
The degree of a monomial is defined as the sum of all the exponents of the variables, including the implicit exponents of 1 for the variables which appear without exponent; e.g., in the example of the previous section, the degree is + +.
Jun 29, · Best Answer: Hi, 1. A zero-degree monomial. A or C 2. A fifth-degree monomial. none H is a 5th degree polynomial, but not a monomial 3. A polynomial with two terms. D 4. A polynomial with three terms. H 5. The coefficient of 7a in – 7a3b-3 I 6.
The Status: Resolved. Fifth degree polynomials are also known as quintic polynomials. Quintics have these characteristics: One to five roots. Zero to four extrema. One to three inflection points. No general symmetry.
It takes six points or six pieces of information to describe a quintic function.
Jun 29, · Best Answer: Hi, 1. A zero-degree monomial. A or C 2. A fifth-degree monomial.
none H is a 5th degree polynomial, but not a monomial 3. A polynomial with two terms. D 4. A polynomial with three terms. H 5. The coefficient of 7a in – 7a3b-3 I 6. The Status: Resolved. 9x 5 - 2x 3x 4 - 2 - This 4 term polynomial has a leading term to the fifth degree and a term to the fourth degree.
It is called a fifth degree polynomial. 3x 3 - This is a one term algebraic expression which is actually referred to as a monomial.